Square Root Calculator › Square root of 103
Square Root of 103
√103 ≈ 10.148892
103 is not a perfect square, so √103 is an irrational number that is approximately 10.148892. In simplified radical form, √103 = √103.
√103 lies between √100 = 10 and √121 = 11.
| Number | 103 |
| Square root (decimal) | 10.148892 |
| Simplified radical | √103 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 103
103 = 103. This is what determines the simplified radical: for √103 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √103 is already in simplest radical form as √103.
Estimating √103 by hand
√103 falls between √100 = 10 and √121 = 11, so it starts at 10.something. The Babylonian method refines that guess by averaging it with 103 ÷ the guess:
| Step | Estimate |
| Start | 10 |
| Step 1 | 10.15 |
| Step 2 | 10.148892 |
| Step 3 | 10.148892 |
After 3 steps the estimate is 10.148892, matching √103 ≈ 10.148892.
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Frequently asked questions
Is 103 a perfect square?
No, 103 is not a perfect square, so its square root is irrational and approximately 10.148892.
What is the square root of 103 in simplest radical form?
√103 = √103 in simplest radical form.